G Kenton Paulino got the start and racked up a career-best 18 points, and C LaMarcus Aldridge finished with 19 points and nine boards.
"Kenton is a smart player," said coach Rick Barnes. "He did a good job of getting us organized early. He set us up and did a good job of getting the ball inside."
The Horns had little problem scoring on the Buffaloes (10-2) but looked even more impressive defensively, limiting Colorado to just 22-of-71 (31.0 percent) from the field.
"We want to create an identity within the Big 12 and college basketball," said Paulino. "We want people to know we are a defensive team and know we can stop them. That has always been a part of Texas Basketball. Defensive stops create offensive opportunities."
Aldridge knocked down three straight jumpers to put Texas on the board with a 6-0 lead to start the contest. After a pair of F Brad Buckman free throws, Paulino connected on a three pointer to give Texas an 11-2 edge.
The Texas bench got into the action early in the game with C Connor Atchley and G A.J. Abrams scoring a pair of baskets, and after Tucker tipped in a loose ball and followed with a lay up, the Horns held onto their nine-point lead.
Abrams later added two baskets from behind the arc to push the lead to 29-14. Abrams finished the day with eight points and five assists, while the Horns shot a combined 8-of-20 (40.0 percent) from three point land.
G Daniel Gibson, who finished with 14 points, got his first score of the day on a three pointer with three minutes left in the half to start a 10-2 Texas run. Tucker then rolled in a lay up and the Horns entered the break with a 43-24 lead.
Aldridge brought Texas out of the break with a dunk and followed with a lay up and free throw to start the second half. After Gibson tacked on two quick treys and Buckman drained a pair of free throws, Texas claimed a 25-point lead.
Tucker then connected on two jumpers and two shots from the charity stripe to kick start an 11-3 Texas run with just under 10 minutes left. After a Paulino three pointer and lay up, Tucker finished the game off with a lay up of his own to seal the 25-point victory.
Despite scoring at least 100 points in two of the last three games, Colorados offense struggled all day to find space against the Texas defense.
"We did a good job defensively," said Barnes. "We have improved a lot on that side of the court."
The victory in the conference opener gives the Horns momentum heading deeper into Big 12 play.
"It was a big point to start out strong, because last year we did not to a good job of that," said Tucker. "We really want to win the Big 12 this year. Tonight we came out and fought hard."
Texas travels to Iowa State Monday for another Big 12 contest at 8 p.m.